Problem: Solve for $n$, $- \dfrac{5n - 10}{4n - 4} = \dfrac{1}{10} $
Multiply both sides of the equation by $4n - 4$ $ -(5n - 10) = \dfrac{4n - 4}{10} $ Multiply both sides of the equation by $10$ $ -10(5n - 10) = 4n - 4 $ $-50n + 100 = 4n - 4$ $100 = 54n - 4$ $104 = 54n$ $54n = 104$ $n = \dfrac{104}{54}$ Simplify. $n = \dfrac{52}{27}$